Chemically strengthened glass-based articles are formed by subjecting glass-based substrates to a chemical modification to improve at least one strength-related characteristic, such as hardness, resistance to fracture, etc. Chemically strengthened glass-based articles have found particular use as cover glasses for display-based electronic devices, especially hand-held devices such as smart phones and tablets.
In one method, the chemical strengthening is achieved by an ion-exchange (IOX) process whereby ions in the matrix of a glass-based substrate (“native ions” or “substrate ions”) are replaced by externally introduced (i.e., replacement or in-diffused) ions, e.g., from a molten bath. The strengthening generally occurs when the replacement ions are larger than the native ions (e.g., Na+ or Li+ ions replaced by K+ ions). The IOX process gives rise to an IOX region in the glass that extends from the article surface into the matrix. The IOX region defines within the matrix a refractive index profile having a depth of layer (DOL) that represents a size, thickness or “deepness” of the IOX region as measured relative to the article surface. The refractive index profile also defines stress-related characteristics, including a stress profile, a surface stress, a depth of compression, a center tension, a birefringence, etc. The refractive index profile can also define in the glass-based article an optical waveguide that supports a number m of guided modes for light of a given wavelength when the refractive index profile meets certain criteria known in the art.
Prism-coupling systems and methods can be used to measure the spectrum of the guided modes of the planar optical waveguide formed in the glass-based IOX article to characterize one or more properties of the IOX region, such as the refractive index profile and the aforementioned stress-related characteristics. This technique has been used to measure properties of glass-based IOX articles used for a variety of applications, such as for chemically strengthened covers for displays (e.g., for smart phones). Such measurements are used for quality control purposes to ensure that the IOX region has the intended characteristics and falls within the select design tolerances for each of the selected characteristics for the given application.
While prism-coupling systems and methods can be used for many types of conventional glass-based IOX articles, such methods do not work as well and sometimes do not work at all on certain glass-based IOX articles. For example, certain types of IOX glass-based articles are actual dual IOX (DIOX) glass-based articles formed by first and second ion diffusions that give rise to a two-part profile. The first part (first region) is immediately adjacent the substrate surface and has a relatively steep slope, while the second segment (second region) extends deeper into the substrate but has a relatively shallow slope. The first region is referred to as the spike region or just “spike,” while the second region is referred to as the deep region. The optical waveguide is defined by both the spike region and the deep region.
Such two-region profiles result in a relatively large spacing between low-order modes, which have a relatively high effective index, and a very small spacing between high-order modes, which have a relatively low effective index close to the critical angle, which defines the boundary or transition between total-internal reflection (TIR) for guided modes and non-TIR for so-called leaky modes. In a mode spectrum, the critical angle can also be called the “critical angle transition” for convenience. It can happen that a guided mode can travel only in the spike region of the optical waveguide. A guided or leaky mode traveling only in the spike region makes it difficult if not impossible to distinguish between light that is guided only in the spike region and light that is guided in the deep region.
Determining the precise location of the critical angle from the mode spectrum for a glass-based IOX article having a two-region profile is problematic because guided modes that reside close to the critical angle distort the intensity profile at the critical angle transition. This in turn distorts the calculation of the fractional number of mode fringes, and hence the calculation of the depth of the spike region and stress-related parameters, including the calculation of the compressive stress at the bottom of the spike region, which is referred to as the “knee stress” and is denoted CSk.
As it turns out, the knee stress CSk is an important property of a glass-based IOX article and its measurement can be used for quality control in large-scale manufacturing of chemically strengthened glass-based articles. Unfortunately, the above-described measurement problems impose severe restrictions when using a prism-coupling system to make measurements of IOX articles for quality control because an accurate estimation of the knee stress CSk requires that the critical angle transition be accurately established for both the transverse electric (TE) and transverse magnetic (TM) guided modes.